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q.scm
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(load "mk.scm")
(define eval-expo
(lambda (exp env val)
(conde
((fresh (v)
(== `(quote ,v) exp)
(not-in-envo 'quote env)
(noo 'closure v)
(== v val)))
((fresh (a*)
(== `(list . ,a*) exp)
(not-in-envo 'list env)
(noo 'closure a*)
(proper-listo a* env val)))
((symbolo exp) (lookupo exp env val))
((fresh (rator rand x body env^ a)
(== `(,rator ,rand) exp)
(eval-expo rator env `(closure ,x ,body ,env^))
(eval-expo rand env a)
(eval-expo body `((,x . ,a) . ,env^) val)))
((fresh (x body)
(== `(lambda (,x) ,body) exp)
(symbolo x)
(not-in-envo 'lambda env)
(== `(closure ,x ,body ,env) val))))))
(define not-in-envo
(lambda (x env)
(conde
((fresh (y v rest)
(== `((,y . ,v) . ,rest) env)
(=/= y x)
(not-in-envo x rest)))
((== '() env)))))
(define proper-listo
(lambda (exp env val)
(conde
((== '() exp)
(== '() val))
((fresh (a d t-a t-d)
(== `(,a . ,d) exp)
(== `(,t-a . ,t-d) val)
(eval-expo a env t-a)
(proper-listo d env t-d))))))
(define lookupo
(lambda (x env t)
(fresh (rest y v)
(== `((,y . ,v) . ,rest) env)
(conde
((== y x) (== v t))
((=/= y x) (lookupo x rest t))))))
(test-check "4 thrines"
(run 4 (x)
(fresh (p q r)
(=/= p q)
(=/= q r)
(=/= r p)
(eval-expo p '() q)
(eval-expo q '() r)
(eval-expo r '() p)
(== `(,p ,q ,r) x)))
'(((''((lambda (_.0)
(list 'quote (list 'quote (list _.0 (list 'quote _.0)))))
'(lambda (_.0)
(list 'quote (list 'quote (list _.0 (list 'quote _.0))))))
'((lambda (_.0)
(list 'quote (list 'quote (list _.0 (list 'quote _.0)))))
'(lambda (_.0)
(list 'quote (list 'quote (list _.0 (list 'quote _.0))))))
((lambda (_.0)
(list 'quote (list 'quote (list _.0 (list 'quote _.0)))))
'(lambda (_.0)
(list 'quote (list 'quote (list _.0 (list 'quote _.0)))))))
(=/= ((_.0 . closure)) ((_.0 . list)) ((_.0 . quote)))
(sym _.0))
((''((lambda (_.0)
(list
'quote
(list
'quote
(list ((lambda (_.1) _.0) '_.2) (list 'quote _.0)))))
'(lambda (_.0)
(list
'quote
(list
'quote
(list ((lambda (_.1) _.0) '_.2) (list 'quote _.0))))))
'((lambda (_.0)
(list
'quote
(list
'quote
(list ((lambda (_.1) _.0) '_.2) (list 'quote _.0)))))
'(lambda (_.0)
(list
'quote
(list
'quote
(list ((lambda (_.1) _.0) '_.2) (list 'quote _.0))))))
((lambda (_.0)
(list
'quote
(list
'quote
(list ((lambda (_.1) _.0) '_.2) (list 'quote _.0)))))
'(lambda (_.0)
(list
'quote
(list
'quote
(list ((lambda (_.1) _.0) '_.2) (list 'quote _.0)))))))
(=/= ((_.0 . closure)) ((_.0 . lambda)) ((_.0 . list))
((_.0 . quote)) ((_.1 . _.0)) ((_.1 . closure)))
(no-closure _.2)
(sym _.0 _.1))
(('(list
'(lambda (_.0)
(list
'quote
(list 'list _.0 (list 'quote (list 'quote _.0)))))
'''(lambda (_.0)
(list
'quote
(list 'list _.0 (list 'quote (list 'quote _.0))))))
(list
'(lambda (_.0)
(list
'quote
(list 'list _.0 (list 'quote (list 'quote _.0)))))
'''(lambda (_.0)
(list
'quote
(list 'list _.0 (list 'quote (list 'quote _.0))))))
((lambda (_.0)
(list
'quote
(list 'list _.0 (list 'quote (list 'quote _.0)))))
''(lambda (_.0)
(list
'quote
(list 'list _.0 (list 'quote (list 'quote _.0)))))))
(=/= ((_.0 . closure)) ((_.0 . list)) ((_.0 . quote)))
(sym _.0))
((''((lambda (_.0)
(list
((lambda (_.1) 'quote) '_.2)
(list 'quote (list _.0 (list 'quote _.0)))))
'(lambda (_.0)
(list
((lambda (_.1) 'quote) '_.2)
(list 'quote (list _.0 (list 'quote _.0))))))
'((lambda (_.0)
(list
((lambda (_.1) 'quote) '_.2)
(list 'quote (list _.0 (list 'quote _.0)))))
'(lambda (_.0)
(list
((lambda (_.1) 'quote) '_.2)
(list 'quote (list _.0 (list 'quote _.0))))))
((lambda (_.0)
(list
((lambda (_.1) 'quote) '_.2)
(list 'quote (list _.0 (list 'quote _.0)))))
'(lambda (_.0)
(list
((lambda (_.1) 'quote) '_.2)
(list 'quote (list _.0 (list 'quote _.0)))))))
(=/= ((_.0 . closure)) ((_.0 . lambda)) ((_.0 . list))
((_.0 . quote)) ((_.1 . closure)) ((_.1 . quote)))
(no-closure _.2)
(sym _.0 _.1))))
(test-check "thrines proof"
(let ([p/q/r (caar (run 1 (x)
(fresh (p q r)
(=/= p q)
(=/= q r)
(=/= r p)
(eval-expo p '() q)
(eval-expo q '() r)
(eval-expo r '() p)
(== `(,p ,q ,r) x))))])
(let ([p (car p/q/r)]
[q (cadr p/q/r)]
[r (caddr p/q/r)])
(and
(equal? (eval p) q)
(equal? (eval q) r)
(equal? (eval r) p)
(not (equal? p q))
(not (equal? q r))
(not (equal? r p)))))
#t)